Why is the second harmonic called the first overtone?

In the study of acoustics, the terminology used to describe vibrating systems distinguishes between the fundamental tone and the higher-frequency components that accompany it.

The fundamental tone, which is the lowest frequency produced by a vibrating medium, is referred to as the first harmonic. Any frequency produced above this fundamental is called an overtone. Because the term "overtone" is used specifically to describe frequencies over (above) the fundamental, the counting sequence for overtones begins only after the fundamental has been established.12

Consequently, the naming convention follows this progression:
* The first harmonic is the fundamental tone itself.1
* The second harmonic is the first frequency above the fundamental, thus it is called the first overtone.2
* The third harmonic is the second frequency above the fundamental, making it the second overtone, and so on.2

While "harmonic" is reserved for frequencies that are exact integral multiples of the fundamental frequency, "overtone" is a broader term that can apply to any higher-frequency standing wave, including those that are not exact multiples.12